Stiffness coefficients are critical parameters necessary in a process of evaluating rock mechanical properties using well logging data in unconventional oil-gas reservoirs represented by tight oil and gas, shale oil gas. Stiffness coefficients specifically include parameters, such as C33, C44, C11, C13, and C66 and the like, wherein the logging calculation method of such two stiffness coefficients C66 and C11 is a difficult problem in the field of evaluating rock mechanical properties using well logging data in unconventional oil-gas reservoirs in recent years. In order to solve this difficult problem, the idea previously employed is first inverting horizontal S-wave velocity in the stoneley waves extracted from array acoustic logging information, then calculating C66 by combining it with volume density logging curves, and finally realizing a logging calculation of stiffness coefficients such as C11 and the like by further utilizing an experimental relation among five stiffness coefficients based thereon. There are obvious limitations to this approach, the main reason is stoneley waves are less sensitive to the horizontal S-wave velocity with larger extraction errors and lower confidences in a fast formation. It is pointed out in paper “Determining formation shear-wave transverse isotropy from borehole stoneley-wave measurements, Xiaoming Tang, Geophysics. Vol. 68, No. 1, 2003” that an approach of extracting a horizontal S-wave velocity from stoneley waves for logging applies only to a slow formation. And the process of extracting horizontal S-wave velocity from stoneley waves is also very complicated, those of ordinary skill in the art find it difficult to implement.